From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
To: "Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>,
"Ralph Baker Kearfott" <rbk@xxxxxxxxxxxx>
Cc: <stds-1788@xxxxxxxxxxxxxxxxx>
Subject: Re: What is your philosophy? Tracking or Static?
Date: Wed, 25 May 2011 08:23:31 -0500
There has been a lot of discussion about tracking vs. static
methodologies.
IMHO, it is a bit of a red-herring to couch things in these terms. Both
are
applications of a single FTDIA. The only difference is how pessimism due
to
unrecognized interval dependence is handled in the computation.
I agree that the only difference amounts to the pessimism
with which decorations are computed. But I do not think
the difference is a red herring.
As a low-level hardware standard, I think P1788 needs to be realistic and
mindful of what it can hope to achieve. In my view, to try and
standardize
interval computations in such a way that the non-pessimistic (what I
believe
people are referring to as "static") result is always returned is simply
too
big a problem. If P1788 tries to do this, it will fail.
THIS is the red herring & also is why the former is not.
You see, I'm pretty sure the basic functions of add, subtract,
multiply & divide are all the same WRT their decorations
behavior no matter WHAT your philosophy. It is precisely in
those functions which are NOT likely to find their way into
hardware where the difference matters. (Well, less likely
anyway.)
My understanding is that P1788 is essentially a low-level standard aimed
at
efficient hardware implementations. If this is true, P1788 should
probably
think very carefully about what is realistically computable at the
hardware
level. From my perspective, this clearly leads to the tracking
methodology.
Nate
I agree with your premise (of permitting efficient interval
hardware) but not your conclusion.
If tracking & static are equivalent for the basic functions
then efficient decorations hardware are equivalent for both.
But for those functions for which it makes a difference (say
max or intersection or the like) the tracking philosophy
gives more pessimistic results than the static one. Possibly
much more pessimistic as George's examples suggest.
Don't get me wrong: We will still need something that cleans
decorations for fixed point algorithms like interval Newton's.
But I am coming to believe that it is best to give the
cleanist decorations we can WHEN we can.
This suggests a static approach.
IMHO, of course.
Anyone else?
Dan